Premium
Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations
Author(s) -
Deng YuanBei,
Bai ZhongZhi,
Gao YongHua
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.496
Subject(s) - hermitian matrix , mathematics , conjugate gradient method , iterative method , matrix (chemical analysis) , norm (philosophy) , system of linear equations , moore–penrose pseudoinverse , linear equation , matrix norm , inverse , mathematical analysis , pure mathematics , geometry , mathematical optimization , eigenvalues and eigenvectors , physics , quantum mechanics , materials science , political science , law , composite material
The consistent conditions and the general expressions about the Hermitian solutions of the linear matrix equations AXB = C and ( AX , XB )=( C , D ) are studied in depth, where A , B , C and D are given matrices of suitable sizes. The Hermitian minimum F ‐norm solutions are obtained for the matrix equations AXB = C and ( AX , XB )=( C , D ) by Moore–Penrose generalized inverse, respectively. For both matrix equations, we design iterative methods according to the fundamental idea of the classical conjugate direction method for the standard system of linear equations. Numerical results show that these iterative methods are feasible and effective in actual computations of the solutions of the above‐mentioned two matrix equations. Copyright © 2006 John Wiley & Sons, Ltd.